getOptionLabel is use to show the text in the dropdown

EX: autocomplete array

const top100Films = [
  { title: 'The Shawshank Redemption', year: 1994 },
  { title: 'The Godfather', year: 1972 },
  { title: 'The Godfather: Part II', year: 1974 },
  { title: 'The Dark Knight', year: 2008 }
}

<Autocomplete
  id="combo-box-demo"
  options={top100Films}
  getOptionLabel={(option) => option.year.toString()} // in the dropdown the option text will be year,if we use like option.title then it will show the title of the movie in dropdown
......

getOptionSelected this is use to determine the selected value of given array

<Autocomplete
  id="combo-box-demo"
  options={top100Films}
  getOptionSelected={(option) => option.year === 1994}
....
//this will select all the option which has year as 1994 and make the background of that option darker

demo

getOptionLabel

Like Kalhan said, getOptionLabel sets the string label in the dropdown.
For example:

    const users = [
        { userName: 'bob',  age: 20, message:[...] },
        { userName: 'jane', age: 43, message:[...] },
        { userName: 'joe',  age: 88, message:[...] },
    }

    <Autocomplete
        id="combo-box-demo"
        options={users}
        getOptionLabel={(user) => user.userName }

getOptionSelected

To clarify, getOptionSelected is used to determine if the selected value (i.e. the string in the autocomplete text field when you select an item from the dropdown) matches an option (in this case, user object) from the options array.

According to the Material-ui docs, getOptionSelected has the following signature, where option is the option to test and value is the value to test against:

function(option: T, value: T) => boolean

As an example, by using getOptionSelected, I can get the full user object when an element is selected from the dropdown (also avoids warnings such as, "The value provided to Autocomplete is invalid...")

    const users = [
        { userName: 'bob',  age: 20, message:[...] },
        { userName: 'jane', age: 43, message:[...] },
        { userName: 'joe',  age: 88, message:[...] },
    }

    <Autocomplete
        id="combo-box-demo"
        options={users}
        getOptionLabel={(user) => user.userName }
        getOptionSelected={(option, value) => option.userName === value.userName }
        onChange={(event, newValue) => {
            this.setValue(newValue);
        }}
 
        // more code

    setValue = (newValue) => {
        console.log(newValue); //  { userName: 'jane', age: 43, message:[...] }
    }